S03 
HUM 
afterwards. But it is fufpeCted that, in the original work, 
the numbers were expreifed in Roman or Saxon charac¬ 
ters. Two letters from that enlightened but ill-requited 
prince to ourEdward I. which are prei'erved in the Tower 
of London, have the dates, 1271 and 1278, (till denoted 
by thofe ancient characters. 
In the tenth volume of the Archasologia, the Rev. Mr. 
North has given a fhort account of an almanac preferved 
in the library of Benet-college, Cambridge, and con¬ 
taining a table of eclipfes for the cycle between 1330 to 
1348. There is prefixed to it a very brief explication of 
the ufeof numerals, and the principles of the denary no¬ 
tation ; from which we may fee how imperfectly the prac¬ 
tice of thofe ciphers was then underftood. The figures 
are of the oldeft form, but differ not materially from the 
prefent, except that the four has a looped (hape, and the 
five and feven are turned about to the left and to the 
right. The one, two, three, and four, are likewife, per¬ 
haps for elucidation, re prefen ted by fo many dots, thus, 
. .. while five, fix, feven, and eight, are figni- 
fied by a femicircle or inverted j, with the addition of . 
correfponding dots; j j. j : Q.‘. Nine is denoted by 
o ; ten by the fame character with adafh drawn acrofs it; 
and twenty, thirty, or forty, by this laft fymbol re¬ 
peated. 
As a farther evidence of the inaccurate conceptions 
which prevailed refpeCting the ufe of the digits in the 
fourteenth century, w’e may refer to the mixture of Sax¬ 
on and Arabic numerals which was copied from fome 
French manufcripts by Mabillon. The Saxon p, figni- 
fying ten, is repeatedly combined with the ordinary 
figures, thus p, p, JC 3 > pH and ppp, ITU!, are immedi¬ 
ately followed by 302, and 303, which muft have been 
therefore intended to fignify thirty-two and thirty-three, 
the force of the cipher not being yet rightly underftood. 
We fubjoin another fpecimen of the Roman or Saxon 
numerals till then ufed. In the accounts of the Scottifh 
Exchequer for the year 1331, the fum of 6896I. 5s. 5d. 
ftated as paid to the king of England, is thus marked : 
vj viij.iiij.xvj.ij. v.s. v.S. It may be obferved, that, in 
Scotland, the contraction for a thoufand, is ftill ufed 
in the dates of charters, and other legal inftruments. 
One of the oldeft authentic dates in the numeral cha¬ 
racters is that of the year 1375, which appears written 
by the hand of the famous Petrarch on a copy of St. A11- 
guftine, that had belonged to that diltinguilhed poet and 
philofopher. The ufe of thofe characters had now be¬ 
gun to fpread in Europe, but was ftill confined to men 
of learning. We have feen a fhort trad in the Ger¬ 
man language, entitled Dc Algorifmo, and bearing the 
date 1390, which explained, with great brevity, the 
digital notation and the elementary rules of arithmetic. 
What is very remarkable, the characters, in their ear- 
lieft form, are ranged thus, o, 9, 8,7,6, 5,4, 3, a, 1, from 
right to left, the order which the Arabians would na¬ 
turally follow-. But it was not very eafy to comprehend 
at firft the precife force of the cipher, which, infignificant 
by itfelf, only ferves to determine the rank and value of 
the other digits. The word zero, derived from an Arabic 
word tfaphara, denoting vacuity, is fufficiently expreflive; 
yet a fort of myftery, which has imprinted its trace on 
language, feemed to hang over the practice ; for we ftill 
fpeak of deciphering, and of writing in cipher, in allufion 
to fome dark or concealed art. 
After the digits had come to fupply the place of the 
Roman numerals, a very confiderable time probably 
elapfed before they were generally adopted in calculation. 
The modern pradice of arithmetic was unknown in Eng¬ 
land till about the middle of the fixteenth century; 
and the lower orders, imitating the clerks of a former 
age, were ftill accuftomed to reckon with the help of 
counters, or mcgrym-fiones. In Shakefpear’s comedy of 
the Winter’s Tale, written at the commencement of the 
B E R. 
feventeenth century, the Clown, ftaggered with a very 
fimple multiplication, exclaims that lie will “ try it with 
counters.” 
Arithmetic was long confidered in England as a higher 
branch of fcience; and therefore left, like geometry, to 
be ftudied at the univerfity. Moft of the public gram- 
mar-fchools of the foufh were, on the fuppreffion of the 
monafteries, ereCted a little after the reformation, during 
the fhort but aufpicious reign of Edw-ard VI. They were 
accordingly deftined by their founders merely for teach¬ 
ing the dead languages; and the too-exclufive purfuit of 
the fame fyftem, is now perhaps one of the greateft defects 
in the Engliflt plan of liberal education. 
It cannot be doubted, that the kalendars compofed in 
France or Germany, and lent to the different religious 
houfes, were the means of difperling the knowledge of 
Arabic numerals over Europe. The library of the Uni¬ 
verfity of Edinburgh has a very curious almanac, w-hich 
was prefented to it, with a number of other valuable 
traffs, by the celebrated Drummond of Hawthornden, 
beautifully written on vellum, with moft of the figures in 
Vermillion. It is calculated efpecially for the year 1482 ; 
but contains the fucceflion of lunar phafes for three cy¬ 
cles, 1475, 1494, and 1513, with the vifible eclipfes of 
the fun and moon, from 1482 to 1530 inclufive. 
The college-accounts in the Englifh univerfities were 
generally kept in the Roman numerals, till the early part 
of the fixteenth century ; nor in the parifh-regifters were 
the Arabic characters adopted before the year 1600. The 
oldeft date which we have met with in Scotland is that of 
1490, which occurs in the rent-roll of the diocefe of St. 
Andrew’s, the change from Roman to Arabic numerals 
occurring, with a correfponding alteration in the form of 
the writing, near the end of the volume. 
Of the different Scales of Numbers. 
In the common or denary fcale of notation, the value 
of every digit increafes from the right hand tow-ards the 
left in a ten-fold proportion ; thus, mu is the fame as 
ioooo-^-iooo-|-ioo-|-io-j-i, and fo on for others ; the dis¬ 
tance of any figure from the right indicating the power 
of 10, and the digit itfelf the number of thofe powers in¬ 
tended to be exprelfed ; on which obvious principle it is 
evident, that any number whatever may be reprefented 
with eafe and fimplicity. But, fince any other number or 
radix might have been alfumed inftead often, the curious 
reader will enquire how it happened that this in particu¬ 
lar Ihould have been fele&ed as the almoft-univerfal radix 
by nations totally unconnected and unknown to each 
other: for even many rude nations, particularly amongft' 
the inhabitants of the iflands in the South Sea, who have 
fcarcely any notions of a regular fyftem of arithmetic, 
yet have a method of dividing their numbers into periods 
of tens; and the fame has been obferved with regard to 
the natives of.New Holland, and fome other newly-difco- 
vered countries. This fingular coincidence between na¬ 
tions totally unknown to each other, has given rife to ■ 
many philofophical fpeculations, from the. time of Arifto- 
tle to the prefent day, though it feems to be now uni- 
verfally fuppofed to have had its origin in the formation 
of man ; that is, to the circumftance of his pofleffing ten 
fingers, by the aid of which, in all probability, calcula¬ 
tion, or at leaft numbering, was firft effected ; as we fee 
children, in making their firft efforts in computation, 
have recourfe to this means of afiifting their memories; 
and hence we may infer, that the prefent divifion of 
numbers into periods of tens had its origin as foon as 
numbering was firft attempted ; that is, as foon as men 
began to affociate with each other. But it muft not 
thence be inferred, that the mode of notation in prefent 
ufe followed neceffarily from this divifion ; of the con¬ 
trary of which we may be convinced by attending to the 
arithmetic of the Greeks, who, notwithftanding they 
made ufe of the fame- divifion, had no idea of our pre¬ 
fent 
